Incorrect Constraint In Both Single and Multiperiod Optimization

[tyler-abbot]

Both the single period and multiperiod optimization policies include the self-financing condition as a constraint. However, the self-financing condition in the program is only $\sum_i u_t^i = 0$, but should include the costs as well: $\sum_i u_t^i + \phi(u_t)= 0$.

[kch382001]

I could be wrong. I think in the original paper(can be found at this link: https://stanford.edu/~boyd/papers/pdf/cvx_portfolio.pdf), on page 50, it is mentioned that by ignoring the cost in self-finance constraint, we allow portfolio to propagate forward. And since the costs are already taken into account in objective function, the output weights should somewhat reflect the impact of cost.

[enzbus]

Hello @tyler-abbot, @kch382001 is correct that condition you mention is simplified to sum $\Sigma_i u = 0$ in order to make the problem convex. The costs are indeed taken into account in the objective, and in practice the effect of the simplification is negligible (but necessary for solvability).